Functions Questions with Solutions

$f\left(x\right)=\sqrt{{log}_{1/4}\left(\frac{5x-x^2}{4}\right)}$, find the domain of $f\left(x\right)$.

If $f:\left[0,3\right]\to \left[1,29\right]$ and $f\left(x\right)=2x^3-15x^2+36x+1$, then $f\left(x\right)$ is

Let $f\left(x\right)=1$ if $\left|x\right|\le 1$ and $f\left(x\right)=0$ if $\left|x\right|>1$; and $g\left(x\right)=2-x^2$ if $\left|x\right|\le 2$ and $g\left(x\right)=2$ if $\left|x\right|>2$. If $h\left(x\right)=f\left[g\left(x\right)\right]$, then an interval in which $h\left(x\right)=1$ for all values of $x$ in that interval is:

The range of $f\left(x\right)=cos\left({log}_{e}x\right)$ is

The range of the function $f\left(x\right)=\frac{x+2}{|x+2|},x\ne -2$ is

The domain of the function $logf\left(x\right)=\sqrt{{log}_{10}\frac{{log}_{10}x}{2\left(3-{log}_{10}x\right)}}$

The graph of the function $f\left(x\right)={log}_e\left(x^3+\sqrt{x^6+1}\right)$ is symmetric about

If $f\left(x\right)$ is a polynomial of degree 4 such that $f\left(n\right)=n+1$ for $n=1,2,3,4$ and $f\left(0\right)=25$, then find $f\left(5\right)$.

A real valued function f is defined as $f\left(x\right)=-1$ for $-2\le x\le 0$ and $f\left(x\right)=x-1$ for $0<x\le 2$. Which of the following statements is FALSE?

If the function $f:[1,\infty )\to [1,\infty )$ is defined by $f\left(x\right)=2^{x\left(x-1\right)}$, then $f^{-1}\left(x\right)$ is

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections from $A$ to $B$ is

If $f\left(x\right)$ is a polynomial satisfying $f\left(x\right)f\left(\frac{1}{x}\right)=f\left(x\right)+f\left(\frac{1}{x}\right)$ and $f\left(3\right)=28$, then $f\left(4\right)$ is

If $f\left(x\right)+f\left(1-x\right)=2$, then the value of $f\left(\frac{1}{2001}\right)+f\left(\frac{2}{2001}\right)+\cdots +f\left(\frac{2000}{2001}\right)$ is

Inverse of the function $f\left(x\right)=\frac{{10}^x-{10}^{-x}}{{10}^x+{10}^{-x}}$ is

The domain of the function $f\left(x\right)=\frac{{cos}^{-1}x}{\left[x\right]}$ is (where $\left[x\right]$ is the greatest integer not exceeding $x$)

The function $f\left(x\right)=log\left(x+\sqrt{x^2+1}\right)$ is

The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

Which of the following functions is the inverse of itself?

The number of real solutions of the equation $sin\left(e^x\right)=5^x+5^{-x}$ is

The number of onto (surjective) functions from A to B, if n(A) = 6 and n(B) = 3, is